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There is a difference between "on the string" staccato and "off the string" staccato with a host of subtle variations (such as spiccato, slurred-staccato, martele, and many others.)
The type of staccato you use depends on the context and the sound that either your or someone else is looking for.
I would consult a bass player for the correct way to perform ...

Well, it's like a slow tremolo so you definitely want to alternate fingers. Thumb - Middle - Thumb - Middle is a good general-purpose tremolo fingering. To do this easily, you should pull your thumb a little under the palm, almost touching the middle finger. The wrist should be straight but not rigid. You descend upon the keyboard, leading with the thumb. ...

I concur with @slim regarding this being a phrase marking, and not a slur or legato mark.
I think the reason for it being there at all is to indicate that the two groups of three notes (F, A, D) are not to be phrased as such - rather, the semiquavers are to be phrased together in such a way as to stand apart from the D that follows.
Without the phrase ...

It seems to me that a pair of notes cannot be both legato and staccato at the same time.
The only explanation that makes sense to me is that these are not slurs but phrase marks.
Per Wikipedia:
The slur is not to be confused with two other similar musical symbols.
The tie is a curved line that links two notes of the same pitch to
show that their ...

This could be an instance of portato. Via wikipedia:
Portato (Italian, past participle of portare, "to carry") in music
denotes a smooth, pulsing articulation and is often notated by adding
dots under slur markings.
Portato, also known as articulated legato or slurred staccato or
semi-staccato or mezzo-staccato, that means "moderately ...

I agree with slim and Widor that this is a phrase mark. However, it is possible to play both legato and staccato at the same time. Legato means "tied together", and as Widor says you want these notes to be "phrased together"; those concepts are obviously closely related and, depending on the interpretation, may be considered one and the same. I'd disagree ...

I'll be honest: I'm not a double bass player. However, from my observation of those who are, I can say that lifting the bow seems to be 'the done thing'.
A quick Google of 'double bass staccato' gave me this: http://www.talkbass.com/forum/f5/staccato-bowing-579305/
I trust that will be of more use to you.